The Existence of BIB Designs ORIGINAL ARTICLES

Received: 22 July 1997 Revised: 24 June 1998 Accepted: 28 September 1998 DOI :
10.1007/s101149900030

Cite this article as: Chang, Y. Acta Math Sinica (2000) 16: 103. doi:10.1007/s101149900030 Abstract Given any positive integers k ≥ 3 and λ, let c (k , λ) denote the smallest integer such that v ∈B (k , λ) for every integer v ≥c (k , λ) that satisfies the congruences λv (v − 1) ≡ 0(mod k (k − 1)) and λ(v − 1) ≡ 0(mod k − 1). In this article we make an improvement on the bound of c (k , λ) provided by Chang in [4] and prove that \(
c{\left( {k,\lambda } \right)} \leqslant \exp {\left\{ {k^{{3k^{6} }} } \right\}}
\) . In particular, \(
c{\left( {k,1} \right)} \leqslant \exp {\left\{ {k^{{k^{2} }} } \right\}}
\) .

Keywords Wilson’s theorem Balanced incomplete block design PBD-closed

1991 MR Subject Classification 05B Supported by NSFC Grant No. 19701002 and Huo Yingdong Foundation

References 1.

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MATH CrossRef 2.

Yanxun Chang. A bound for Wilson's theorem (I). J Combin Design, 1995, 3: 25-39

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© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations 1. Institute of Mathematics Northern Jiaotong University Beijing 100044 P.R. China